Twenty-two US senators have signed a letter to President Donald Trump, triggering an investigation and determination of whether human rights sanctions should be imposed over the disappearance of a Saudi journalist.

Jamal Khashoggi disappeared on 2 October after visiting a Saudi consulate in Turkey.

In the letter, the senators said they had triggered a provision of the Global Magnitsky Human Rights Accountability Act requiring the president to determine whether a foreign person is responsible for a gross human rights violation.

"Our expectation is that in making your determination you will consider any relevant information, including with respect to the highest ranking officials in the Government of Saudi Arabia," they said.

Under the terms of the act, a report must be made in 120 days with a decision on he imposition of sanctions on whoever was responsible.

Mr Trump has said he wanted to get to the bottom of the matter, increasing the pressure on Saudi officials to provide information on what happened.

Mr Khashoggi is a legal resident of the United States and a Washington Post columnist. He has been a prominent critic of Saudi policies.

Turkish sources have said they believe Mr Khashoggi was killed inside the consulate and then removed.

Saudi officials have dismissed the allegations as baseless.

Mr Khashoggi had entered the consulate to get documents for his planned marriage. His Turkish fiance, Hatice Cengiz, who was waiting outside, said he never re-appeared.

Mr Trump, in comments in the Oval Office, told reporters he had raised Mr Khashoggi's case with Saudi Arabia "at the highest level" and more than once in recent days.

"We're demanding everything," Mr Trump said when asked if he was demanding information from the Saudis.  

"We want to see what's going on. It’s a very serious situation for us and for this White House ... We want to get to the bottom of it."

He said he and his wife, Melania, expect to invite Ms Cengiz to the White House soon.

"People saw him go in and didn't see him come out. We're going to take a very serious look at it. It's a terrible thing," Mr Trump said.

"This is a bad situation. We cannot let this happen, to reporters, to anybody. We can't let this happen."

In another sign the White House was stepping up pressure, White House national security adviser John Bolton and White House senior adviser Jared Kushner, Mr Trump's son-in-law, spoke to Saudi Crown Prince Mohammed bin Salman yesterday.

The White House also said U.S. Secretary of State Mike Pompeo followed up with his own call to the Crown Prince, who had forged close ties to the administration, especially Mr Kushner.